Abstract
Let Pn denote the set of positive integers which are prime to n. Let Bn be the n-th Bernoulli number. For any prime p>5 and integer r≥2, we prove that∑l1+l2+⋯+l5=prl1,⋯,l5∈Pp1l1l2l3l4l5≡−5!6pr−1Bp−5(modpr). This gives an extension of a family of curious congruences found by the author, Cai and Zhao.
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